1214 lines
32 KiB
Fortran
1214 lines
32 KiB
Fortran
!!******************************************************************************
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!!
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!! module: EVOLUTION - handling the time evolution of the block structure
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!!
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!! Copyright (C) 2008-2011 Grzegorz Kowal <grzegorz@amuncode.org>
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!!
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!!******************************************************************************
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!!
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!! This file is part of the AMUN code.
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!!
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!! This program is free software; you can redistribute it and/or
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!! modify it under the terms of the GNU General Public License
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!! as published by the Free Software Foundation; either version 2
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!! of the License, or (at your option) any later version.
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!!
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!! This program is distributed in the hope that it will be useful,
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!! but WITHOUT ANY WARRANTY; without even the implied warranty of
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!! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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!! GNU General Public License for more details.
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!!
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!! You should have received a copy of the GNU General Public License
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!! along with this program; if not, write to the Free Software Foundation,
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!! Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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!!
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!!******************************************************************************
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!!
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!
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module evolution
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implicit none
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integer, save :: n
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real , save :: t, dt, dtn, dxmin
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contains
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!
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!===============================================================================
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!
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! evolve: subroutine sweeps over all leaf blocks and performs one step time
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! evolution for each according to the selected integration scheme
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!
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!===============================================================================
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!
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subroutine evolve()
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use blocks , only : block_data, list_data
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use boundaries, only : boundary_variables
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#ifdef CONSERVATIVE
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use boundaries, only : boundary_correct_fluxes
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#endif /* CONSERVATIVE */
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#ifdef REFINE
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use config , only : maxlev
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#endif /* REFINE */
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use mesh , only : update_mesh
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use timer , only : start_timer, stop_timer
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#ifdef FORCE
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use forcing , only : fourier_transform, evolve_forcing
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use variables , only : idn, imz
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#endif /* FORCE */
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implicit none
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! local variables
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!
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type(block_data), pointer :: pblock
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real :: cm
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!
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!-------------------------------------------------------------------------------
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!
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! start the evolution timer
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!
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call start_timer(2)
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#ifdef FORCE
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! perform the Fourier transform of the velocity field
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!
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pblock => list_data
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do while (associated(pblock))
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if (pblock%meta%leaf) &
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call fourier_transform(pblock%meta%level &
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, pblock%meta%xmin, pblock%meta%ymin, pblock%meta%zmin &
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, pblock%u(idn:imz,:,:,:))
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pblock => pblock%next ! assign pointer to the next block
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end do
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! evolve the forcing source terms by the time interval dt
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!
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call evolve_forcing(dt)
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#endif /* FORCE */
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! iterate over all data blocks and perform one step of time evolution
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!
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pblock => list_data
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do while (associated(pblock))
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! check if this block is a leaf
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!
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#ifdef CONSERVATIVE
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if (pblock%meta%leaf) &
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#ifdef EULER
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call flux_euler(pblock)
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#endif /* EULER */
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#ifdef RK2
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call flux_rk2(pblock)
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#endif /* RK2 */
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#ifdef RK3
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call flux_rk3(pblock)
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#endif /* RK3 */
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#else /* CONSERVATIVE */
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if (pblock%meta%leaf) &
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#ifdef EULER
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call evolve_euler(pblock)
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#endif /* EULER */
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#ifdef RK2
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call evolve_rk2(pblock)
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#endif /* RK2 */
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#ifdef RK3
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call evolve_rk3(pblock)
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#endif /* RK3 */
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#endif /* CONSERVATIVE */
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! assign pointer to the next block
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!
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pblock => pblock%next
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end do
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#ifdef CONSERVATIVE
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! correct the numerical fluxes between neighboring blocks which are at different
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! levels
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!
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call boundary_correct_fluxes()
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! update solution using numerical fluxes stored in data blocks
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!
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pblock => list_data
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do while (associated(pblock))
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! check if this block is a leaf and update its conserved variables using
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! corrected numerical fluxes
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!
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if (pblock%meta%leaf) call update_solution(pblock)
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! assign pointer to the next block
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!
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pblock => pblock%next
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end do
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#endif /* CONSERVATIVE */
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! update boundaries
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!
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call boundary_variables()
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#ifdef REFINE
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! chec if we need to perform the refinement step
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!
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if (maxlev .gt. 1) then
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! check refinement and refine
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!
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call update_mesh()
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! update boundaries
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!
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call boundary_variables()
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end if ! maxlev > 1
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#endif /* REFINE */
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! find new time step
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!
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call find_new_timestep()
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! stop the evolution timer
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!
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call stop_timer(2)
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!
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!-------------------------------------------------------------------------------
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!
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end subroutine evolve
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!
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!===============================================================================
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!
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! find_new_timestep: subroutine updates the maximum speed among the leafs and
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! calculates new time step
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!
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!===============================================================================
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!
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subroutine find_new_timestep()
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use blocks , only : block_meta, block_data, list_meta, list_data
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use config , only : maxlev
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#ifdef MPI
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use mpitools, only : mallreducemaxr
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#endif /* MPI */
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use coords , only : adx, ady, adz
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use scheme , only : maxspeed, cmax
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use timer , only : start_timer, stop_timer
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#ifdef VISCOSITY
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use config , only : visc
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#endif /* VISCOSITY */
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#if defined MHD && defined RESISTIVITY
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use config , only : ueta
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#endif /* MHD & RESISTIVITY */
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implicit none
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! local variables
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!
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real :: cm
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integer(kind=4) :: lev
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! local pointers
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!
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type(block_meta), pointer :: pmeta
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type(block_data), pointer :: pdata
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!
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!-------------------------------------------------------------------------------
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!
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! start the evolution timer
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!
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call start_timer(6)
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! reset the maximum speed, and highest level
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!
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cmax = 1.0d-16
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lev = 1
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! if maxlev > 1, find the highest level
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!
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if (maxlev .gt. 1) then
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! iterate over all meta blocks and find the highest level with leafs
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!
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pmeta => list_meta
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do while (associated(pmeta))
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! check if the metablock is a leaf, if so obtaind the highest level
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!
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if (pmeta%leaf) lev = max(lev, pmeta%level)
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! associate the pointer with the next block
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!
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pmeta => pmeta%next
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end do ! meta blocks
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! find the smallest spacial step
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!
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#if NDIMS == 2
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dxmin = min(adx(lev), ady(lev))
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#endif /* NDIMS == 2 */
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#if NDIMS == 3
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dxmin = min(adx(lev), ady(lev), adz(lev))
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#endif /* NDIMS == 3 */
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end if ! maxlev > 1
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! iterate over all data blocks in order to find the maximum speed among them
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!
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pdata => list_data
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do while (associated(pdata))
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! check if this block is a leaf
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!
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if (pdata%meta%leaf) then
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! find the maximum level occupied by blocks (can be smaller than maxlev)
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!
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! obtain the maximum speed for the current block
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!
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cm = maxspeed(pdata%u(:,:,:,:))
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! compare global and local maximum speeds
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!
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cmax = max(cmax, cm)
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end if ! leaf
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! assiociate the pointer with the next block
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!
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pdata => pdata%next
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end do
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#ifdef MPI
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! reduce the maximum speed over all processes
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!
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call mallreducemaxr(cmax)
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#endif /* MPI */
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! calcilate new time step
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!
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dtn = dxmin / max(cmax, 1.0d-16)
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#ifdef VISCOSITY
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dtn = min(dtn, 0.5d0 * dxmin * dxmin / max(1.0d-16, visc))
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#endif /* VISCOSITY */
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#if defined MHD && defined RESISTIVITY
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dtn = min(dtn, 0.5d0 * dxmin * dxmin / max(1.0d-16, ueta))
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#endif /* MHD & RESISTIVITY */
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! stop the evolution timer
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!
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call stop_timer(6)
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!
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!-------------------------------------------------------------------------------
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!
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end subroutine find_new_timestep
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#ifdef CONSERVATIVE
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!
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!===============================================================================
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!
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! update_solution: subroutine performs an one step update of the conserved
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! variables for the given data block using the integrated
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! numerical fluxes stored in the same data block
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!
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!===============================================================================
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!
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subroutine update_solution(pblock)
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use blocks , only : block_data
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use config , only : im, jm, km
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use coords , only : adxi, adyi, adzi
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#if defined MHD && defined GLM
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use config , only : alpha_p
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use scheme , only : cmax
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use variables, only : iph
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#endif /* MHD & GLM */
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#ifdef FORCE
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use forcing , only : real_forcing
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use variables, only : inx, iny, inz
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use variables, only : idn, imx, imy, imz
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#ifdef ADI
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use variables, only : ien
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#endif /* ADI */
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#endif /* FORCE */
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#ifdef SHAPE
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use problem , only : update_shapes
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#endif /* SHAPE */
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implicit none
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! input arguments
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!
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type(block_data), pointer, intent(inout) :: pblock
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! local variables
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!
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real :: dxi, dyi, dzi
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#if defined MHD && defined GLM
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real :: decay
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#endif /* MHD & GLM */
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#ifdef FORCE
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! local arrays
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!
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real, dimension( 3,im,jm,km) :: f
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#ifdef ADI
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real, dimension( im,jm,km) :: ek, dek
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#endif /* ADI */
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#endif /* FORCE */
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!
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!-------------------------------------------------------------------------------
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!
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! prepare dxi, dyi, and dzi
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!
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dxi = adxi(pblock%meta%level)
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dyi = adyi(pblock%meta%level)
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#if NDIMS == 3
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dzi = adzi(pblock%meta%level)
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#endif /* NDIMS == 3 */
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! perform update of conserved variables of the given block using its fluxes
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!
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call advance_solution(pblock%u(:,:,:,:), pblock%f(:,:,:,:,:), dxi, dyi, dzi)
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#if defined MHD && defined GLM
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! evolve Psi due to the source term
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!
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decay = exp(- alpha_p * cmax * dt / dxmin)
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pblock%u(iph,:,:,:) = decay * pblock%u(iph,:,:,:)
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#endif /* MHD & GLM */
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#ifdef FORCE
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! obtain the forcing terms in real space
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!
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call real_forcing(pblock%meta%level, pblock%meta%xmin, pblock%meta%ymin &
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, pblock%meta%zmin, f(:,:,:,:))
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#ifdef ADI
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! calculate kinetic energy before adding the forcing term
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!
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ek(:,:,:) = 0.5d0 * (pblock%u(imx,:,:,:)**2 + pblock%u(imy,:,:,:)**2 &
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+ pblock%u(imz,:,:,:)**2) / pblock%u(idn,:,:,:)
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#endif /* ADI */
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! update momenta due to the forcing terms
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!
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pblock%u(imx,:,:,:) = pblock%u(imx,:,:,:) &
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+ pblock%u(idn,:,:,:) * f(inx,:,:,:)
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pblock%u(imy,:,:,:) = pblock%u(imy,:,:,:) &
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+ pblock%u(idn,:,:,:) * f(iny,:,:,:)
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pblock%u(imz,:,:,:) = pblock%u(imz,:,:,:) &
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+ pblock%u(idn,:,:,:) * f(inz,:,:,:)
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#ifdef ADI
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! calculate kinetic energy after adding the forcing term
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!
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dek(:,:,:) = 0.5d0 * (pblock%u(imx,:,:,:)**2 + pblock%u(imy,:,:,:)**2 &
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+ pblock%u(imz,:,:,:)**2) / pblock%u(idn,:,:,:) - ek(:,:,:)
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! update total energy with the injected one
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!
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pblock%u(ien,:,:,:) = pblock%u(ien,:,:,:) + dek(:,:,:)
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#endif /* ADI */
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#endif /* FORCE */
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#ifdef SHAPE
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! update solid shapes
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!
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call update_shapes(pblock, t)
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#endif /* SHAPE */
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!-------------------------------------------------------------------------------
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!
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end subroutine update_solution
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!
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!===============================================================================
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!
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! advance_solution: subroutine performs an one step update of the conserved
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! variables array using the numerical fluxes passed as an
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! argument
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!
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!===============================================================================
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!
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subroutine advance_solution(u, f, dxi, dyi, dzi)
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use config , only : im, jm, km
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use variables, only : nqt, nfl
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use variables, only : inx, iny, inz
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#ifdef MHD
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use variables, only : ibx, ibz
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#ifdef GLM
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use scheme , only : cmax
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use variables, only : iph
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#endif /* GLM */
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#endif /* MHD */
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implicit none
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! input arguments
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!
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real, dimension( nqt,im,jm,km), intent(inout) :: u
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real, dimension(NDIMS,nqt,im,jm,km), intent(in) :: f
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real :: dxi, dyi, dzi
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! local variables
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!
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integer :: i, j, k, im1, jm1, km1
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real :: dhx, dhy, dhz
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#if defined MHD && defined GLM
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real :: ch2
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#endif /* MHD & GLM */
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! local arrays
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!
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real, dimension(nqt,im,jm,km) :: du
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!
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!-------------------------------------------------------------------------------
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!
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! prepare dxi, dyi, and dzi
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!
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dhx = dt * dxi
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dhy = dt * dyi
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#if NDIMS == 3
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dhz = dt * dzi
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#endif /* NDIMS == 3 */
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! reset the increment array du
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!
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du(:,:,:,:) = 0.0d0
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! perform update along the X direction
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!
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do i = 1, im
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im1 = max(1, i - 1)
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du(:,i,:,:) = du(:,i,:,:) + dhx * (f(inx,:,im1,:,:) - f(inx,:,i,:,:))
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end do
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! perform update along the Y direction
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!
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do j = 1, jm
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jm1 = max(1, j - 1)
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du(:,:,j,:) = du(:,:,j,:) + dhy * (f(iny,:,:,jm1,:) - f(iny,:,:,j,:))
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end do
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#if NDIMS == 3
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! perform update along the Z direction
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!
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do k = 1, km
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km1 = max(1, k - 1)
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du(:,:,:,k) = du(:,:,:,k) + dhz * (f(inz,:,:,:,km1) - f(inz,:,:,:,k))
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end do
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#endif /* NDIMS == 3 */
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! update the solution for the fluid variables
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!
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u( 1:nfl,:,:,:) = u( 1:nfl,:,:,:) + du( 1:nfl,:,:,:)
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#ifdef MHD
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! update the solution for the magnetic variables
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!
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u(ibx:ibz,:,:,:) = u(ibx:ibz,:,:,:) + du(ibx:ibz,:,:,:)
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#ifdef GLM
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! calculate c_h^2
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!
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ch2 = cmax * cmax
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! update the solution for the scalar potential Psi
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!
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u(iph,:,:,:) = u(iph,:,:,:) + ch2 * du(iph,:,:,:)
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#endif /* GLM */
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#endif /* MHD */
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!-------------------------------------------------------------------------------
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!
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end subroutine advance_solution
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#ifdef EULER
|
|
!
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!===============================================================================
|
|
!
|
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! flux_euler: subroutine performs the first order integration of the numerical
|
|
! flux
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!
|
|
!===============================================================================
|
|
!
|
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subroutine flux_euler(pblock)
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|
|
use blocks , only : block_data
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use coords , only : adxi, adyi, adzi
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use scheme , only : update_flux
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|
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implicit none
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|
|
|
! input arguments
|
|
!
|
|
type(block_data), pointer, intent(inout) :: pblock
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|
|
|
! local variables
|
|
!
|
|
real :: dxi, dyi, dzi
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|
!
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
! prepare dxi, dyi, and dzi
|
|
!
|
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dxi = adxi(pblock%meta%level)
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dyi = adyi(pblock%meta%level)
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dzi = adzi(pblock%meta%level)
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|
|
! 1st step of integration
|
|
!
|
|
call update_flux(pblock%u(:,:,:,:), pblock%f(:,:,:,:,:), dxi, dyi, dzi)
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
end subroutine flux_euler
|
|
#endif /* EULER */
|
|
#ifdef RK2
|
|
!
|
|
!===============================================================================
|
|
!
|
|
! flux_rk2: subroutine performs integration of the numerical flux using
|
|
! the second order Runge-Kutta method
|
|
!
|
|
!===============================================================================
|
|
!
|
|
subroutine flux_rk2(pblock)
|
|
|
|
use blocks , only : block_data
|
|
use config , only : im, jm, km
|
|
use coords , only : adxi, adyi, adzi
|
|
use scheme , only : update_flux
|
|
use variables, only : nqt
|
|
|
|
implicit none
|
|
|
|
! input arguments
|
|
!
|
|
type(block_data), pointer, intent(inout) :: pblock
|
|
|
|
! local variables
|
|
!
|
|
real :: dxi, dyi, dzi
|
|
|
|
! local arrays
|
|
!
|
|
real, dimension( nqt,im,jm,km) :: u
|
|
real, dimension(NDIMS,nqt,im,jm,km) :: f0, f1
|
|
!
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
! prepare dxi, dyi, and dzi
|
|
!
|
|
dxi = adxi(pblock%meta%level)
|
|
dyi = adyi(pblock%meta%level)
|
|
dzi = adzi(pblock%meta%level)
|
|
|
|
! copy the initial state to the local array u
|
|
!
|
|
u(:,:,:,:) = pblock%u(:,:,:,:)
|
|
|
|
! calculate fluxes at the moment t
|
|
!
|
|
call update_flux(u(:,:,:,:), f0(:,:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! advance the solution to (t + dt) using computed fluxes in this substep
|
|
!
|
|
call advance_solution(u(:,:,:,:), f0(:,:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! calculate fluxes at the moment (t + dt)
|
|
!
|
|
call update_flux(u(:,:,:,:), f1(:,:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! calculate the time averaged flux
|
|
!
|
|
pblock%f(:,:,:,:,:) = 0.5d0 * (f0(:,:,:,:,:) + f1(:,:,:,:,:))
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
end subroutine flux_rk2
|
|
#endif /* RK2 */
|
|
#ifdef RK3
|
|
!
|
|
!===============================================================================
|
|
!
|
|
! flux_rk3: subroutine performs integration of the numerical flux using
|
|
! the third order Runge-Kutta method
|
|
!
|
|
!===============================================================================
|
|
!
|
|
subroutine flux_rk3(pblock)
|
|
|
|
use blocks , only : block_data
|
|
use config , only : im, jm, km
|
|
use coords , only : adxi, adyi, adzi
|
|
use scheme , only : update_flux
|
|
use variables, only : nqt
|
|
|
|
implicit none
|
|
|
|
! input arguments
|
|
!
|
|
type(block_data), pointer, intent(inout) :: pblock
|
|
|
|
! local variables
|
|
!
|
|
real :: dxi, dyi, dzi
|
|
|
|
! local arrays
|
|
!
|
|
real, dimension( nqt,im,jm,km) :: u
|
|
real, dimension(NDIMS,nqt,im,jm,km) :: f0, f1, f2
|
|
!
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
! prepare dxi, dyi, and dzi
|
|
!
|
|
dxi = adxi(pblock%meta%level)
|
|
dyi = adyi(pblock%meta%level)
|
|
dzi = adzi(pblock%meta%level)
|
|
|
|
! copy the initial state to the local array u
|
|
!
|
|
u(:,:,:,:) = pblock%u(:,:,:,:)
|
|
|
|
! calculate fluxes at the moment t
|
|
!
|
|
call update_flux(u(:,:,:,:), f0(:,:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! advance the solution to (t + dt) using computed fluxes in this substep
|
|
!
|
|
call advance_solution(u(:,:,:,:), f0(:,:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! calculate fluxes at the moment (t + dt)
|
|
!
|
|
call update_flux(u(:,:,:,:), f1(:,:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! copy the initial state to the local array u
|
|
!
|
|
u(:,:,:,:) = pblock%u(:,:,:,:)
|
|
|
|
! average fluxes from t and t + dt and prepare for half step update
|
|
!
|
|
f2(:,:,:,:,:) = 0.25d0 * (f0(:,:,:,:,:) + f1(:,:,:,:,:))
|
|
|
|
! advance the solution to (t + dt/2) using computed flux
|
|
!
|
|
call advance_solution(u(:,:,:,:), f2(:,:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! calculate fluxes at the moment (t + dt/2)
|
|
!
|
|
call update_flux(u(:,:,:,:), f2(:,:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! calculate the time averaged flux using Gauss formula
|
|
!
|
|
pblock%f(:,:,:,:,:) = (f0(:,:,:,:,:) + f1(:,:,:,:,:) &
|
|
+ 4.0d0 * f2(:,:,:,:,:)) / 6.0d0
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
end subroutine flux_rk3
|
|
#endif /* RK3 */
|
|
#else /* CONSERVATIVE */
|
|
#ifdef EULER
|
|
!
|
|
!===============================================================================
|
|
!
|
|
! evolve_euler: subroutine evolves the current block using Euler integration
|
|
!
|
|
!===============================================================================
|
|
!
|
|
subroutine evolve_euler(pblock)
|
|
|
|
use blocks , only : block_data
|
|
use config , only : im, jm, km
|
|
#ifdef FORCE
|
|
use forcing , only : real_forcing
|
|
#endif /* FORCE */
|
|
use coords , only : adxi, adyi, adzi
|
|
#ifdef SHAPE
|
|
use problem , only : update_shapes
|
|
#endif /* SHAPE */
|
|
use scheme , only : update, cmax
|
|
use variables, only : nqt, nfl
|
|
#ifdef MHD
|
|
use variables, only : ibx, ibz
|
|
#ifdef GLM
|
|
use config , only : alpha_p
|
|
use variables, only : iph
|
|
#endif /* GLM */
|
|
#endif /* MHD */
|
|
#ifdef FORCE
|
|
use variables, only : idn, imx, imy, imz
|
|
#ifdef ADI
|
|
use variables, only : ien
|
|
#endif /* ADI */
|
|
#endif /* FORCE */
|
|
|
|
implicit none
|
|
|
|
! input arguments
|
|
!
|
|
type(block_data), pointer, intent(inout) :: pblock
|
|
|
|
! local variables
|
|
!
|
|
real :: dxi, dyi, dzi, ch2
|
|
#if defined MHD && defined GLM
|
|
real :: decay
|
|
#endif /* MHD & GLM */
|
|
|
|
! local arrays
|
|
!
|
|
real, dimension(nqt,im,jm,km) :: du
|
|
#ifdef FORCE
|
|
real, dimension( 3,im,jm,km) :: f
|
|
#ifdef ADI
|
|
real, dimension( im,jm,km) :: ek, dek
|
|
#endif /* ADI */
|
|
#endif /* FORCE */
|
|
!
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
! prepare dxi, dyi, and dzi
|
|
!
|
|
dxi = adxi(pblock%meta%level)
|
|
dyi = adyi(pblock%meta%level)
|
|
dzi = adzi(pblock%meta%level)
|
|
|
|
! 1st step of integration
|
|
!
|
|
call update(pblock%u(:,:,:,:), du(:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! update the solution for the fluid variables
|
|
!
|
|
pblock%u(1:nfl,:,:,:) = pblock%u(1:nfl,:,:,:) + dt * du(1:nfl,:,:,:)
|
|
|
|
#ifdef MHD
|
|
! update the solution for the magnetic variables
|
|
!
|
|
pblock%u(ibx:ibz,:,:,:) = pblock%u(ibx:ibz,:,:,:) + dt * du(ibx:ibz,:,:,:)
|
|
|
|
#ifdef GLM
|
|
! calculate c_h^2
|
|
!
|
|
ch2 = cmax * cmax
|
|
|
|
! update the solution for the scalar potential Psi
|
|
!
|
|
pblock%u(iph,:,:,:) = pblock%u(iph,:,:,:) + ch2 * dt * du(iph,:,:,:)
|
|
|
|
! evolve Psi due to the source term
|
|
!
|
|
decay = exp(- alpha_p * cmax * dt / dxmin)
|
|
pblock%u(iph,:,:,:) = decay * pblock%u(iph,:,:,:)
|
|
#endif /* GLM */
|
|
#endif /* MHD */
|
|
#ifdef FORCE
|
|
! obtain the forcing terms in real space
|
|
!
|
|
call real_forcing(pblock%meta%level, pblock%meta%xmin, pblock%meta%ymin &
|
|
, pblock%meta%zmin, f(:,:,:,:))
|
|
|
|
#ifdef ADI
|
|
! calculate kinetic energy before adding the forcing term
|
|
!
|
|
ek(:,:,:) = 0.5d0 * (pblock%u(imx,:,:,:)**2 + pblock%u(imy,:,:,:)**2 &
|
|
+ pblock%u(imz,:,:,:)**2) / pblock%u(idn,:,:,:)
|
|
#endif /* ADI */
|
|
|
|
! update momenta due to the forcing terms
|
|
!
|
|
pblock%u(imx,:,:,:) = pblock%u(imx,:,:,:) + pblock%u(idn,:,:,:) * f(1,:,:,:)
|
|
pblock%u(imy,:,:,:) = pblock%u(imy,:,:,:) + pblock%u(idn,:,:,:) * f(2,:,:,:)
|
|
pblock%u(imz,:,:,:) = pblock%u(imz,:,:,:) + pblock%u(idn,:,:,:) * f(3,:,:,:)
|
|
|
|
#ifdef ADI
|
|
! calculate kinetic energy after adding the forcing term
|
|
!
|
|
dek(:,:,:) = 0.5d0 * (pblock%u(imx,:,:,:)**2 + pblock%u(imy,:,:,:)**2 &
|
|
+ pblock%u(imz,:,:,:)**2) / pblock%u(idn,:,:,:) - ek(:,:,:)
|
|
|
|
! update total energy with the injected one
|
|
!
|
|
pblock%u(ien,:,:,:) = pblock%u(ien,:,:,:) + dek(:,:,:)
|
|
#endif /* ADI */
|
|
#endif /* FORCE */
|
|
|
|
#ifdef SHAPE
|
|
! restrict update in a defined shape
|
|
!
|
|
call update_shapes(pblock, t)
|
|
#endif /* SHAPE */
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
end subroutine evolve_euler
|
|
#endif /* EULER */
|
|
#ifdef RK2
|
|
!
|
|
!===============================================================================
|
|
!
|
|
! evolve_rk2: subroutine evolves the current block using the 2nd order
|
|
! Runge-Kutta method
|
|
!
|
|
!===============================================================================
|
|
!
|
|
subroutine evolve_rk2(pblock)
|
|
|
|
use blocks , only : block_data
|
|
use config , only : im, jm, km
|
|
#ifdef FORCE
|
|
use forcing , only : real_forcing
|
|
#endif /* FORCE */
|
|
use coords , only : adxi, adyi, adzi
|
|
#ifdef SHAPE
|
|
use problem , only : update_shapes
|
|
#endif /* SHAPE */
|
|
use scheme , only : update, cmax
|
|
use variables, only : nqt, nfl
|
|
#ifdef MHD
|
|
use variables, only : ibx, ibz
|
|
#ifdef GLM
|
|
use config , only : alpha_p
|
|
use variables, only : iph
|
|
#endif /* GLM */
|
|
#endif /* MHD */
|
|
#ifdef FORCE
|
|
use variables, only : idn, imx, imy, imz
|
|
#ifdef ADI
|
|
use variables, only : ien
|
|
#endif /* ADI */
|
|
#endif /* FORCE */
|
|
|
|
implicit none
|
|
|
|
! input arguments
|
|
!
|
|
type(block_data), pointer, intent(inout) :: pblock
|
|
|
|
! local variables
|
|
!
|
|
real :: dxi, dyi, dzi, ch2
|
|
#if defined MHD && defined GLM
|
|
real :: decay
|
|
#endif /* MHD & GLM */
|
|
|
|
! local arrays
|
|
!
|
|
real, dimension(nqt,im,jm,km) :: u1, du
|
|
#ifdef FORCE
|
|
real, dimension( 3,im,jm,km) :: f
|
|
#ifdef ADI
|
|
real, dimension( im,jm,km) :: ek, dek
|
|
#endif /* ADI */
|
|
#endif /* FORCE */
|
|
!
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
! prepare dxi, dyi, and dzi
|
|
!
|
|
dxi = adxi(pblock%meta%level)
|
|
dyi = adyi(pblock%meta%level)
|
|
dzi = adzi(pblock%meta%level)
|
|
|
|
!! 1st step of integration
|
|
!!
|
|
call update(pblock%u(:,:,:,:), du(:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! update the solution for the fluid variables
|
|
!
|
|
u1(1:nfl,:,:,:) = pblock%u(1:nfl,:,:,:) + dt * du(1:nfl,:,:,:)
|
|
|
|
#ifdef MHD
|
|
! update the solution for the magnetic variables
|
|
!
|
|
u1(ibx:ibz,:,:,:) = pblock%u(ibx:ibz,:,:,:) + dt * du(ibx:ibz,:,:,:)
|
|
|
|
#ifdef GLM
|
|
! calculate c_h^2
|
|
!
|
|
ch2 = cmax * cmax
|
|
|
|
! update the solution for the scalar potential Psi
|
|
!
|
|
u1(iph,:,:,:) = pblock%u(iph,:,:,:) + ch2 * dt * du(iph,:,:,:)
|
|
|
|
#endif /* GLM */
|
|
#endif /* MHD */
|
|
! 2nd step of integration
|
|
!
|
|
call update(u1(:,:,:,:), du(:,:,:,:), dxi, dyi, dzi)
|
|
|
|
! update the solution for the fluid variables
|
|
!
|
|
pblock%u(1:nfl,:,:,:) = 0.5d0 * (pblock%u(1:nfl,:,:,:) &
|
|
+ u1(1:nfl,:,:,:) + dt * du(1:nfl,:,:,:))
|
|
|
|
#ifdef MHD
|
|
! update the solution for the magnetic variables
|
|
!
|
|
pblock%u(ibx:ibz,:,:,:) = 0.5d0 * (pblock%u(ibx:ibz,:,:,:) &
|
|
+ u1(ibx:ibz,:,:,:) + dt * du(ibx:ibz,:,:,:))
|
|
|
|
#ifdef GLM
|
|
! update the solution for the scalar potential Psi
|
|
!
|
|
pblock%u(iph,:,:,:) = 0.5d0 * (pblock%u(iph,:,:,:) &
|
|
+ u1(iph,:,:,:) + ch2 * dt * du(iph,:,:,:))
|
|
|
|
! evolve Psi due to the source term
|
|
!
|
|
decay = exp(- alpha_p * cmax * dt / dxmin)
|
|
pblock%u(iph,:,:,:) = decay * pblock%u(iph,:,:,:)
|
|
|
|
#endif /* GLM */
|
|
#endif /* MHD */
|
|
#ifdef FORCE
|
|
! obtain the forcing terms in real space
|
|
!
|
|
call real_forcing(pblock%meta%level, pblock%meta%xmin, pblock%meta%ymin &
|
|
, pblock%meta%zmin, f(:,:,:,:))
|
|
|
|
#ifdef ADI
|
|
! calculate kinetic energy before adding the forcing term
|
|
!
|
|
ek(:,:,:) = 0.5d0 * (pblock%u(imx,:,:,:)**2 + pblock%u(imy,:,:,:)**2 &
|
|
+ pblock%u(imz,:,:,:)**2) / pblock%u(idn,:,:,:)
|
|
#endif /* ADI */
|
|
|
|
! update momenta due to the forcing terms
|
|
!
|
|
pblock%u(imx,:,:,:) = pblock%u(imx,:,:,:) + pblock%u(idn,:,:,:) * f(1,:,:,:)
|
|
pblock%u(imy,:,:,:) = pblock%u(imy,:,:,:) + pblock%u(idn,:,:,:) * f(2,:,:,:)
|
|
pblock%u(imz,:,:,:) = pblock%u(imz,:,:,:) + pblock%u(idn,:,:,:) * f(3,:,:,:)
|
|
|
|
#ifdef ADI
|
|
! calculate kinetic energy after adding the forcing term
|
|
!
|
|
dek(:,:,:) = 0.5d0 * (pblock%u(imx,:,:,:)**2 + pblock%u(imy,:,:,:)**2 &
|
|
+ pblock%u(imz,:,:,:)**2) / pblock%u(idn,:,:,:) - ek(:,:,:)
|
|
|
|
! update total energy with the injected one
|
|
!
|
|
pblock%u(ien,:,:,:) = pblock%u(ien,:,:,:) + dek(:,:,:)
|
|
#endif /* ADI */
|
|
#endif /* FORCE */
|
|
|
|
#ifdef SHAPE
|
|
! restrict update in a defined shape
|
|
!
|
|
call update_shapes(pblock, t)
|
|
|
|
#endif /* SHAPE */
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
end subroutine evolve_rk2
|
|
#endif /* RK2 */
|
|
#ifdef RK3
|
|
!
|
|
!===============================================================================
|
|
!
|
|
! evolve_rk3: subroutine evolves the current block using the 3rd order
|
|
! Runge-Kutta method
|
|
!
|
|
!===============================================================================
|
|
!
|
|
subroutine evolve_rk3(pblock)
|
|
|
|
use blocks , only : block_data
|
|
use config , only : im, jm, km
|
|
#ifdef FORCE
|
|
use forcing , only : real_forcing
|
|
#endif /* FORCE */
|
|
use coords , only : adxi, adyi, adzi
|
|
#ifdef SHAPE
|
|
use problem , only : update_shapes
|
|
#endif /* SHAPE */
|
|
use scheme , only : update, cmax
|
|
use variables, only : nqt, nfl
|
|
#ifdef MHD
|
|
use variables, only : ibx, ibz
|
|
#ifdef GLM
|
|
use config , only : alpha_p
|
|
use variables, only : iph
|
|
#endif /* GLM */
|
|
#endif /* MHD */
|
|
#ifdef FORCE
|
|
use variables, only : idn, imx, imy, imz
|
|
#ifdef ADI
|
|
use variables, only : ien
|
|
#endif /* ADI */
|
|
#endif /* FORCE */
|
|
|
|
implicit none
|
|
|
|
! input arguments
|
|
!
|
|
type(block_data), pointer, intent(inout) :: pblock
|
|
|
|
! local variables
|
|
!
|
|
real :: dxi, dyi, dzi
|
|
#if defined MHD && defined GLM
|
|
real :: decay, ch2
|
|
#endif /* MHD & GLM */
|
|
|
|
! local arrays
|
|
!
|
|
real, dimension(nqt,im,jm,km) :: u1, du
|
|
#ifdef FORCE
|
|
real, dimension( 3,im,jm,km) :: f
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#ifdef ADI
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real, dimension( im,jm,km) :: ek, dek
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#endif /* ADI */
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#endif /* FORCE */
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! parameters
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!
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real, parameter :: f4 = 1.0d0 / 4.0d0, f3 = 1.0d0 / 3.0d0
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!
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!-------------------------------------------------------------------------------
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!
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! prepare dxi, dyi, and dzi
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!
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dxi = adxi(pblock%meta%level)
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dyi = adyi(pblock%meta%level)
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dzi = adzi(pblock%meta%level)
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!! 1st step of integration
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!!
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call update(pblock%u(:,:,:,:), du(:,:,:,:), dxi, dyi, dzi)
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! update the solution for the fluid variables
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!
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u1(1:nfl,:,:,:) = pblock%u(1:nfl,:,:,:) + dt * du(1:nfl,:,:,:)
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#ifdef MHD
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! update the solution for the magnetic variables
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!
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u1(ibx:ibz,:,:,:) = pblock%u(ibx:ibz,:,:,:) + dt * du(ibx:ibz,:,:,:)
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#ifdef GLM
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! calculate c_h^2
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!
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ch2 = cmax * cmax
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! update the solution for the scalar potential Psi
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!
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u1(iph,:,:,:) = pblock%u(iph,:,:,:) + ch2 * dt * du(iph,:,:,:)
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#endif /* GLM */
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#endif /* MHD */
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!! 2nd step of integration
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!!
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call update(u1(:,:,:,:), du(:,:,:,:), dxi, dyi, dzi)
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! update the solution for the fluid variables
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!
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u1(1:nfl,:,:,:) = f4 * (3.0d0 * pblock%u(1:nfl,:,:,:) &
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+ u1(1:nfl,:,:,:) + dt * du(1:nfl,:,:,:))
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#ifdef MHD
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! update the solution for the magnetic variables
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!
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u1(ibx:ibz,:,:,:) = f4 * (3.0d0 * pblock%u(ibx:ibz,:,:,:) &
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+ u1(ibx:ibz,:,:,:) + dt * du(ibx:ibz,:,:,:))
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#ifdef GLM
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! update the solution for the scalar potential Psi
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!
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u1(iph,:,:,:) = f4 * (3.0d0 * pblock%u(iph,:,:,:) &
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+ u1(iph,:,:,:) + ch2 * dt * du(iph,:,:,:))
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#endif /* GLM */
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#endif /* MHD */
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!! 3rd step of integration
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!!
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call update(u1(:,:,:,:), du(:,:,:,:), dxi, dyi, dzi)
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! update the solution for the fluid variables
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!
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pblock%u(1:nfl,:,:,:) = f3 * (pblock%u(1:nfl,:,:,:) &
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+ 2.0d0 * (u1(1:nfl,:,:,:) + dt * du(1:nfl,:,:,:)))
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#ifdef MHD
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! update the solution for the magnetic variables
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!
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pblock%u(ibx:ibz,:,:,:) = f3 * (pblock%u(ibx:ibz,:,:,:) &
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+ 2.0d0 * (u1(ibx:ibz,:,:,:) + dt * du(ibx:ibz,:,:,:)))
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#ifdef GLM
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! update the solution for the scalar potential Psi
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!
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pblock%u(iph,:,:,:) = f3 * (pblock%u(iph,:,:,:) &
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+ 2.0d0 * (u1(iph,:,:,:) + ch2 * dt * du(iph,:,:,:)))
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! evolve analytically Psi due to the source term
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!
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decay = exp(- alpha_p * cmax * dt / dxmin)
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pblock%u(iph,:,:,:) = decay * pblock%u(iph,:,:,:)
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#endif /* GLM */
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#endif /* MHD */
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#ifdef FORCE
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! obtain the forcing terms in real space
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!
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call real_forcing(pblock%meta%level, pblock%meta%xmin, pblock%meta%ymin &
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, pblock%meta%zmin, f(:,:,:,:))
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#ifdef ADI
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! calculate kinetic energy before adding the forcing term
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!
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ek(:,:,:) = 0.5d0 * (pblock%u(imx,:,:,:)**2 + pblock%u(imy,:,:,:)**2 &
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+ pblock%u(imz,:,:,:)**2) / pblock%u(idn,:,:,:)
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#endif /* ADI */
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! update momenta due to the forcing terms
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!
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pblock%u(imx,:,:,:) = pblock%u(imx,:,:,:) + pblock%u(idn,:,:,:) * f(1,:,:,:)
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pblock%u(imy,:,:,:) = pblock%u(imy,:,:,:) + pblock%u(idn,:,:,:) * f(2,:,:,:)
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pblock%u(imz,:,:,:) = pblock%u(imz,:,:,:) + pblock%u(idn,:,:,:) * f(3,:,:,:)
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#ifdef ADI
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! calculate kinetic energy after adding the forcing term
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!
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dek(:,:,:) = 0.5d0 * (pblock%u(imx,:,:,:)**2 + pblock%u(imy,:,:,:)**2 &
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+ pblock%u(imz,:,:,:)**2) / pblock%u(idn,:,:,:) - ek(:,:,:)
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! update total energy with the injected one
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!
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pblock%u(ien,:,:,:) = pblock%u(ien,:,:,:) + dek(:,:,:)
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#endif /* ADI */
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#endif /* FORCE */
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#ifdef SHAPE
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! restrict update in a defined shape
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!
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call update_shapes(pblock, t)
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#endif /* SHAPE */
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!-------------------------------------------------------------------------------
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!
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end subroutine evolve_rk3
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#endif /* RK3 */
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#endif /* CONSERVATIVE */
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!
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!===============================================================================
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!
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end module
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